Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Mathematical Concepts”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 559 records · Page 31Linked to original sources
PubMed1993

Myopic astigmatism and simple myopia correction.

A new technique for the treatment of myopic astigmatism and simple myopia correction is described. The technique is based on bioengineering concepts previously studied by the authors that accurately and mathematically describe the transformation of an ellipsoidal surface (astigmatic eye) into a spheroidal one (nonastigmatic eye) by means of minimal cuts (keratotomies). The surgical procedure is described using selected cases to illustrate the alternatives the model can handle. The model itself is not presented because the calculations were done by computer.

Adolescent↗
PubMed1977

On the concept of biomathematics.

The increasing complexity of biological problems and the increase of mathematical means to handle them on the one hand, and the possibility of automatized computation at the other, necessitate a revaluation of the present interactions between biology and mathematics; in this connection interrelations occur which can be divided into three kinds: mathematical biology, biological mathematics, and 'general biomathematics' or methodology of the biomathematical sciences, by which are meant those scientific branches which arise from the said interactions.

Mathematics↗
PubMed1986

[The meaning of statistical data in medical science and their examination--true and false analysis of statistical data].

The subjects which are often encountered in the statistical design and analysis of data in medical science studies were discussed. The five topics examined were: Medical science and statistical methods So-called mathematical statistics and medical science Fundamentals of cross-tabulation analysis of statistical data and inference Exploratory study by multidimensional data analyses Optimal process control of individual, medical science and informatics of statistical data In I, the author's statistico-mathematical idea is characterized as the analysis of phenomena by statistical data. This is closely related to the logic, methodology and philosophy of science. This statistical concept and method are based on operational and pragmatic ideas. Self-examination of mathematical statistics is particularly focused in II and III. In II, the effectiveness of experimental design and statistical testing is thoroughly examined with regard to the study of medical science, and the limitation of its application is discussed. In III the apparent paradox of analysis of cross-tabulation of statistical data and statistical inference is shown. This is due to the operation of a simple two- or three-fold cross-tabulation analysis of (more than two or three) multidimensional data, apart from the sophisticated statistical test theory of association. In IV, the necessity of informatics of multidimensional data analysis in medical science is stressed. In V, the following point is discussed. The essential point of clinical trials is that they are not based on any simple statistical test in a traditional experimental design but on the optimal process control of individuals in the information space of the body and mind, which is based on a knowledge of medical science and the informatics of multidimensional statistical data analysis.

Statistics as Topic↗
PubMed2004

Eigenmobilities in background electrolytes for capillary zone electrophoresis: III. Linear theory of electromigration.

A mathematical model of capillary zone electrophoresis (CZE) based on the conception of eigenmobilities, which are the eigenvalues of a matrix M tied to the linearized governing equations is presented. The model considers CZE systems, where constituents, either analytes or components of the background electrolyte (BGE), are weak electrolytes--acids, bases, or ampholytes. There is no restriction on the number of components nor on the valence of the constituents nor on pH of the BGE. An electrophoretic system with N constituents has N eigenmobilities. In most BGEs one or two eigenmobilities are very close to zero so their corresponding eigenzones move very slowly. However, there are BGEs where no eigenmobility is close to zero. The mathematical model further provides: the transfer ratio, the molar conductivity detection response, and the relative velocity slope. This allows the assessment of the indirect detection, conductivity detection and peak broadening (distortion) due to electromigration dispersion. Also, we present a spectral decomposition of the matrix M to matrices allowing the assessment of the amplitudes of system eigenpeaks (system peaks). Our model predicted the existence of BGEs having no stationary injection zone (or water zone, gap, peak, dip). A common practice of using the injection zone as a marker of the electroosmotic flow must fail in such electrolytes.

Buffers↗
PubMed2006

The impact on oncology of the interaction of radiation therapy and radiobiology.

The quantitative analysis of the cell dose-survival curves, the randomness of cell killing by radiation, the probabilistic basis of the response to irradiation of tumors and normal tissues, the understanding of the biological mechanisms underlying to this response, the rationale for dose-time and fractionation in radiotherapy, the introduction of the concepts of tumor control probability (TCP) and biologically effective dose (BED), the relationships TCP-dose, BED-alpha/beta BED-fraction size and BED-treatment time, the problems associated with the accelerated regeneration of surviving tumor clonogens during the course of fractionated radiotherapy, the new demands of knowledge on oncology and radiation biology derived from heterogeneous dose distributions in conformal radiation therapy programs and the definition of the biological basis of normal tissues tolerance to reirradiation are, probably, the most important contributions of radiobiology to clinical radiotherapy in the last twenty five years. Radiotherapy is today a scientific discipline based on the interplay of mathematics, physics, biology and oncology. The knowledge of the basic concepts of radiobiology is essential for daily radiotherapy practices and for all oncologists. The most efficient use of multimodality treatments in cancer therapy cannot be done without a clear understanding of these principles.

Apoptosis↗
PubMed1977

[Phenomenologic-mathematical modeling of the human-body-length growth through the analysis of growth periods and their quantitative-analytical registration].

The body height growth (of masculine beings) was modelled in a phenomenologic-mathematical manner by partitioning the time course of measured growth curve in parts every of which corresponds to a separated growth period. This partitioning was reached in a natural way so that a superposition of the single spurts yields the whole measured course. Every growth batch will be described in its time course by one term of inverse tangent function. The biological meaning and an explanation of the succession of the growth spurt as an effect of control circuits need further exploratory work. For detailed statements on acceleration phenomena concerning the body height growth this analysis gives possibilities for comparing the single growth spurts of the mean growth process of two populations in question. For measured values given by BROCK (1954) and SALZLER (1967) there are five growth periods in the time intervall reaching from time of conception until the end of the first year. Comparing the mathematical functions of the corresponding growth spurts for these two groups one can conclude that the second spurt (fetal spurt) is responsible for an increase of birth body height and the fourth for an increase of body height in the suckling age of the latter group against the former one.

Adolescent↗
PubMed2005

Language and modeling word problems in mathematics among bilinguals.

The study was conducted to determine whether the language of math word problems would affect how Filipino-English bilingual problem solvers would model the structure of these word problems. Modeling the problem structure was studied using the problem-completion paradigm, which involves presenting problems without the question. The paradigm assumes that problem solvers can infer the appropriate question of a word problem if they correctly grasp its problem structure. Arithmetic word problems in Filipino and English were given to bilingual students, some of whom had Filipino as a first language and others who had English as a first language. The problem-completion data and solution data showed similar results. The language of the problem had no effect on problem-structure modeling. The results were discussed in relation to a more circumscribed view about the role of language in word problem solving among bilinguals. In particular, the results of the present study showed that linguistic factors do not affect the more mathematically abstract components of word problem solving, although they may affect the other components such as those related to reading comprehension and understanding.

Child↗
PubMed2005

Mathematical modelling of radiotherapy strategies for early breast cancer.

Targeted intraoperative radiotherapy (Targit) is a new concept of partial breast irradiation where single fraction radiotherapy is delivered directly to the tumour bed. Apart from logistic advantages, this strategy minimizes the risk of missing the tumour bed and avoids delay between surgery and radiotherapy. It is presently being compared with the standard fractionated external beam radiotherapy (EBRT) in randomized trials. In this paper we present a mathematical model for the growth and invasion of a solid tumour into a domain of tissue (in this case breast tissue), and then a model for surgery and radiation treatment of this tumour. We use the established linear-quadratic (LQ) model to compute the survival probabilities for both tumour cells and irradiated breast tissue and then simulate the effects of conventional EBRT and Targit. True local recurrence of the tumour could arise either from stray tumour cells, or the tumour bed that harbours morphologically normal cells having a predisposition to genetic changes, such as a loss of heterozygosity (LOH) in genes that are crucial for tumourigenesis, e.g. tumour suppressor genes (TSGs). Our mathematical model predicts that the single high dose of radiotherapy delivered by Targit would result in eliminating all these sources of recurrence, whereas the fractionated EBRT would eliminate stray tumour cells, but allow (by virtue of its very schedule) the cells with LOH in TSGs or cell-cycle checkpoint genes to pass on low-dose radiation-induced DNA damage and consequently mutations that may favour the development of a new tumour. The mathematical model presented here is an initial attempt to model a biologically complex phenomenon that has until now received little attention in the literature and provides a 'proof of principle' that it is possible to produce clinically testable hypotheses on the effects of different approaches of radiotherapy for breast cancer.

Brachytherapy↗
PubMedDate not supplied

[A mathematical model of the status of mitochondrial DNA for assessing the effectiveness of energy biosynthesis in mammalian cells].

A concept is advanced according to which the processes of ageing, non-specific pathology and malignant transformation are caused by mutations of mitochondrial DNA which controls protein synthesis of the oxidation phosphorylation system. A mathematical model is plotted for describing the efficiency of the system of energy supply of mammalian cells as a function of accumulation of mtDNA mutations. It is shown that at a definite degree of heterogeneity of mitochondria population malignant transformation proceeds. Explanations are presented of the existence of a latent period between the effect of cancerogenic agent and occurrence of tumour, mechanism of the realization of remote effects of chronic action of low intensity agents (these explanations are absent in modern theories of cancerogenesis and quantitative radiobiology).

Animals↗
PubMedDate not supplied

Cognitive strategy instruction in mathematics for students with learning disabilities.

This article provides a context for understanding and using cognitive strategy instruction to improve students' performance in mathematics. The theoretical and research base for strategy instruction is reviewed, and characteristics of students who have difficulties in mathematics are discussed from a developmental perspective. Then, a practical illustration of cognitive strategy instruction used to assess the teach mathematical problem solving to middle school students with learning disabilities is presented.

Achievement↗
PubMed2003

Abstraction in mathematics.

Some current interpretations of abstraction in mathematical settings are examined from different perspectives, including history and learning. It is argued that abstraction is a complex concept and that it cannot be reduced to generalization or decontextualization only. In particular, the links between abstraction processes and the emergence of new objects are shown. The role that representations have in abstraction is discussed, taking into account both the historical and the educational perspectives. As languages play a major role in mathematics, some ideas from functional linguistics are applied to explain to what extent mathematical notations are to be considered abstract. Finally, abstraction is examined from the perspective of mathematics education, to show that the teaching ideas resulting from one-dimensional interpretations of abstraction have proved utterly unsuccessful.

Concept Formation↗
PubMed1993

A graph theory model of the semantic structure of attitudes.

The semantic structure underlying the attitudes of pretreatment and posttreatment drug addicts was modeled using a network analysis of free word associations. Measures of graph theoretic properties were used to assess structural differences in the associative networks of the two populations. These measures modeled the information processes of associative networks proposed in the spreading activation theory of semantic processing. As expected based on graph theory, the structure of the associative networks of posttreatment subjects was more dense, less constrained, and more hierarchically organized by the self concept. In a test of the network model, the subjects' evaluations of concepts in the associative network were found to be a function of their evaluations of semantically similar concepts. Although preliminary and limited, the results suggest that graph theory may provide a broad mathematical foundation for diverse models of cognitive systems.

Attitude↗
PubMed2004

A simple mathematical model of cooperativity in receptor mosaics based on the "symmetry rule".

The phenomenon of receptor-receptor interactions was hypothesized about 20 years ago. It has been demonstrated by now that receptor-receptor interactions between G-protein coupled receptors (GPCRs) occur at plasma membrane level and result in the reciprocal modulation of their binding characteristics (i.e., cooperativity). One of the most important feature of this phenomenon is the concept of cluster of receptors, or receptor mosaic (RM). However, no proper mathematical approach has still been available to characterize RMs as far as their receptor composition, receptor topography and order of receptor activation inside the RM. This paper tries to fill the gap. A simple mathematical approach to the cooperativity in RMs formed by dimers of identical receptors and/or by iso-receptors is proposed. To this aim the so-called "symmetry rule" has been considered. This approach allows to describe by means of a simple energy function the effects of receptor composition (number of dimers), spatial organisation (respective location of the dimers) and order of activation (order according to which the single receptors are ligated) on the integrative cooperativity (index) of the RMs.

Binding Sites↗
PubMedDate not supplied

Modelling receptor-controlled intracellular calcium oscillators.

This paper presents mathematical models for the hepatocyte calcium oscillator which follow the concepts in a class of informal models developed to account for the striking dependence on the receptor type of several features of the calcium oscillations, in particular the shape and duration of the free calcium transients. The essence of these models is that the transients should be timed by a build-up of activated GTP-binding proteins, which, combined with positive feedback processes and perhaps with cooperative effects, leads to a sudden activation of phospholipase C (PLC), followed by negative feedback processes which switch off the calcium rise and lead to a fall in free calcium back to resting levels. These models predict pulsatile oscillations in inositol (1,4,5)P3 as well as in free calcium. We show that receptor-controlled intracellular calcium oscillators involving an unknown positive feedback pathway onto PLC and negative feedback from protein kinase C (PKC) onto G-proteins and receptors, or negative feedback by stimulation of GTPase activity can simulate many of the features of observed intracellular calcium oscillations. These oscillators exhibit a dependence of frequency on agonist concentration and a dependence of transient duration on receptor and G-protein type. We also show that a PLC-dependent GTPase activating factor (GAF) could provide explanations for some otherwise puzzling features of intracellular calcium oscillations.

Animals↗
PubMed1986

A quantitative dynamic concept of the interphase partition of lipids: application to bile salt-lecithin-cholesterol mixed micelles.

A system is proposed for a quantitative classification of lipids, based on interphase partition coefficients. This system enables calculation of exchanges of lipid molecules between phases. The mass/volume chemical unit mol X cm-3, strictly derived from the CGS system, is used, thus simplifying mathematical relations. Applied to bile salt-lecithin-cholesterol mixed micelles, this dynamic concept gives new insight into the variations of physico-chemical parameters. Experimental results obtained with the glycodesoxycholate and the taurocholate show a striking difference in partition coefficients between aqueous and mixed bile salt-lecithin interfacial phases. A new model applying triangular co-ordinates to a bile salt-lecithin-cholesterol mixed lipid phase is described.

Bile Acids and Salts↗